Police confirmed with Eyewitness News that someone threw the firebomb at the man, who was at a market on Pacific Coast Highway near Pacific Avenue at about 11 p.m. Friday.
Authorities say the victim, a man in his 50s, was taken to a hospital, where he was in serious but stable condition with burns mostly to his lower extremities.
No arrests have been made.
If you have any information that can help investigators, you're asked to call Los Angeles County Crime Stoppers at (800) 222-TIPS or (800) 222-8477.
City News Service contributed to this report.